基于MATLAB仿真的数字信号调制的性能比较和分析

2ASK、2FSK、2PSK数字调制系统的Matlab实现及性能分析比较指导教师:班级：学号：姓名：引言：数字信号有两种传输方式，分别是基带传输方式和调制传输方式，即带通，在实际应用中，因基带信号含有大量低频分量不利于传送，所以必须经过载波和调制形成带通信号，通过数字基带信号对载波某些参量进行控制，使之随机带信号的变化而变化，这这一过程即为数字调制。

数字调制为信号长距离高效传输提供保障，现已广泛应用于生活和生产中。

另外根据控制载波参量方式的不同，数字调制主要有调幅（ASK ），调频(FSK)，调相(PSK) 三种基本形式。

本次课题针对于二进制的2ASK 、2FSK 、2PSK 进行讨论，应用Matlab 矩阵实验室进行仿真，分析和修改，通过仿真系统生成一个人机交互界面，以利于仿真系统的操作。

通过对系统的仿真，更加直观的了解数字调制系统的性能及影响其性能的各种因素，以便于比较，评论和改进。

关键词： 数字，载波，调制，2ASK ，2FSK ，2PSK ，Matlab ，仿真，性能，比较，分析正文：一 .数字调制与解调原理1.1 2ASK（1）2ASK2ASK 就是把频率、相位作为常量，而把振幅作为变量，信息比特是通过载波的幅度来传递的。

由于调制信号只有0或1两个电平，相乘的结果相当于将载频或者关断，或者接通，它的实际意义是当调制的数字信号"1时，传输载波；当调制的数字信号为"0"时，不传输载波。

表达式为： ⎩⎨⎧===001,cos )(2k k c ASK a a t A t s 当，当ω1.2 2FSK2FSK 可以看做是2个不同频率的2ASK 的叠加，其调制与解调方法与2ASK 差不多，主要频率F1和F2，不同的组合产生所要求的2FSK 调制信号。

公式如下：⎩⎨⎧===0cos 1,cos )(212k k FSK a t A a t A t s 当，当ωω1.3 2PSK2PSK以载波的相位变化为基准，载波的相位随数字基带序列信号的1或者0而改变，通常用已经调制完的载波的0或者π表示数据1或者0，每种相位与之一一对应。

二．数字调制技术的仿真实现本课程设计需要借助MATLAB的M文件编程功能，对2ASK.2PSK.2FSK进行调制与解调的设计，并绘制出调制与解调后的波形，误码率的情况分析，软件仿真可在已有平台上实现。

1.2ASK代码主函数close allclear alln=16;fc=1000000; bitRate=1000000;N=50;%noise=ti;noise=10;signal=source(n,N); %生成二进制代码transmittedSignal=askModu(signal,bitRate,fc,N);%调制后信号signal1=gussian(transmittedSignal,noise);%加噪声configueSignal=demoASK(signal1,bitRate,fc,n,N);source代码function sendSignal=source(n,N)sendSignal=randint(1,n)bit=[];for i=1:length(sendSignal)if sendSignal(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(1)plot(1:length(bit),bit),title('transmitting of binary'),grid on;axis([0,N*length(sendSignal),-2,2]);endaskModu代码function transmittedSignal=askModu(signal,bitRate,fc,N)%signal为输入信号，bitrate为bit速率，fc调制信号频率，N %signal=[0 0 1 0 1 1 0 1];% bitRate=1000000;% fc=1000000;% N=32; t=linspace(0,1/bitRate,N);c=sin(2*pi*t*fc);transmittedSignal=[];for i=1:length(signal)transmittedSignal=[transmittedSignal,signal(i)*c];endfigure(2) %画调制图plot(1:length(transmittedSignal),transmittedSignal);title('Modulation of ASK');grid on;figure(3)%画频谱实部m=0:length(transmittedSignal)-1;F=fft(transmittedSignal);plot(m,abs(real(F))),title('ASK_frequency-domain analysis real');grid on;%figure(4)画频谱虚部%plot(m,imag(F));title('ASK_frequency-domain analysis imag');%grid on;endCheckRatePe代码function PeWrong=CheckRatePe(signal1,signal2,s)rights=0;wrongs=0;for ki=1:s-2if(signal1(ki)==signal2(ki))rights=rights+1;elsewrongs=wrongs+1;endendPeWrong=wrongs/(wrongs+rights);enddemoASK代码function bitstream=demoASK(receivedSignal,bitRate,fc,n,N)load numsignal1=receivedSignal;signal2=abs(signal1); %ÕûÁ÷signal3=filter(num1,1,signal2); %LPF,°üÂç¼ì²¨IN=fix(length(num1)/2); %ÑÓ³Ùʱ¼äbitstream=[];LL=fc/bitRate*N;i=IN+LL/2;while (i<=length(signal3)) %Åоöbitstream=[bitstream,signal3(i)>=0.5];i=i+LL;endfigure(6)subplot(3,1,1); %接收波形plot(1:length(signal1),signal1);title('Wave of receivingterminal(including noise)');grid on;subplot(3,1,2);%接收整流后波形plot(1:length(signal2),signal2);title('Wave of commutate');grid on; subplot(3,1,3);%包络检波波形plot(1:length(signal3),signal3);title('Wave of LPF');grid on;bit=[];for i=1:length(bitstream)if bitstream(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(7)%解调后的二进制波形plot(bit),title('binary of receiving terminal'),grid on;axis([0,N*length(bitstream),-2.5,2.5]);endgussian代码%加高斯白噪声function signal=gussian(transmittedSignal,noise)signal=sqrt(2)*transmittedSignal;signal=awgn(signal,noise);figure(5)plot(1:length(signal),signal);title('Wave including noise'),grid on;endfsk主函数代码close allclear alln=16;%二进制代码长度f1=18000000;%频率1f2=6000000;%频率2bitRate=1000000;%bit速率N=50;%码元宽度%noise=ti;noise=10;%家性噪声大小signal=source(n,N);%产生二进制代码transmittedSignal=fskModu(signal,bitRate,f1,f2,N);%调制signal1=gussian(transmittedSignal,noise);%加噪声configueSignal=demoFSK(signal1,bitRate,f1,f2,N);%解调source代码%二进制信号产生函数function sendSignal=source(n,N)sendSignal=randint(1,n)bit=[];for i=1:length(sendSignal)if sendSignal(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(1)plot(bit),title('transmitting of binary'),grid on;axis([0,N*length(sendSignal),-2.5,2.5]);endfskModu代码%频率调制函数function transmittedSignal=fskModu(signal,bitRate,f1,f2,N)t=linspace(0,1/bitRate,N);c1=sin(2*pi*t*f1);%调制信号1c2=sin(2*pi*t*f2);%调制信号2transmittedSignal=[];for i=1:length(signal)%调制if signal(i)==1transmittedSignal=[transmittedSignal,c1];elsetransmittedSignal=[transmittedSignal,c2];endendfigure(2) %画调制后波形图plot(1:length(transmittedSignal),transmittedSignal);title('Modulation of FSK');grid on;figure(3) %画调制后频谱图m=0:length(transmittedSignal)-1;F=fft(transmittedSignal);plot(m,abs(real(F))),title('ASK_frequency-domain analysis real');grid on;enddemoFSK代码function bitstream=demoFSK(receivedSignal,bitRate,f1,f2,N)load numsignal1=receivedSignal;signal2=filter(gaotong,1,signal1); %通过HPF，得到高通分量signal3=abs(signal2); %整流signal3=filter(lowpass,1,signal3); %通过低通，形成包络bitstream=[];IN1=fix(length(lowpass)/2)+fix(length(gaotong)/2); %延迟时间bitstream1=[];LL=N; %每个bit的抽样点数i=IN1 +LL/2;while (i<=length(signal3)) %判决bitstream1=[bitstream1,signal3(i)>=0.5];i=i+LL;endbitstream1figure(5)subplot(3,1,1);plot(1:length(signal1),signal1);title('Wave of receivingterminal(including noise)');grid on;subplot(3,1,2);plot(1:length(signal2),signal2);title('After Passing HPF');grid on; subplot(3,1,3);plot(1:length(signal3),signal3);title('After Passing LPF');grid on;signal4=filter(daitong,1,signal1); %通过BPF得到低频分量signal5=abs(signal4); %整流signal5=filter(lowpass,1,signal5); %通过LPF，形成包络IN2=fix(length(lowpass)/2)+fix(length(daitong)/2); %延迟时间 bitstream2=[];LL=N; %每个bit的的抽样点数i=IN2 +LL/2;while (i<=length(signal5)) %判决bitstream2=[bitstream2,signal5(i)>=0.5];i=i+LL;endbitstream2figure(6)subplot(3,1,1);plot(1:length(signal1),signal1);title('Wave of receivingterminal(including noise)');grid on;subplot(3,1,2);plot(1:length(signal4),signal4);title('After Passing BPF');grid on; subplot(3,1,3);plot(1:length(signal5),signal5);title('After Passing LPF');grid on;for i=1:min(length(bitstream1),length(bitstream2)) %判决if(bitstream1(i)>bitstream2(i))bitstream(i)=1;elsebitstream(i)=0;endendbitstreambit=[]; %接收端波形for i=1:length(bitstream)if bitstream(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(7)plot(bit),title('binary of receiving terminal'),grid on;axis([0,N*length(bitstream),-2.5,2.5]);endCheckRatePe代码function PeWrong=CheckRatePe(signal1,signal2,s)rights=0;wrongs=0;for ki=1:s-2if(signal1(ki)==signal2(ki))rights=rights+1;elsewrongs=wrongs+1;endendPeWrong=wrongs/(wrongs+rights);endgussian代码function signal=gussian(transmittedSignal,noise)signal=sqrt(2)*transmittedSignal;signal=awgn(signal,noise);figure(4)plot(1:length(signal),signal),title('Adding Noise');grid on;end2psk主函数代码close allclear alln=16;%二进制码长fc=1000000;%载波频率bitRate=1000000;信息频率N=50;%码宽noise=10;%信道加性噪声大小signal=source(n,N);生成二进制代码transmittedSignal=bpskModu(signal,bitRate,fc,N);对信号进行调制并进行频谱分析signal1=gussian(transmittedSignal,noise)%加信道噪声configueSignal=demoBPSK(signal1,bitRate,fc,n,N);%信号解调source代码function sendSignal=source(n,N)sendSignal=randint(1,n)bit=[];for i=1:length(sendSignal)if sendSignal(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(1)plot(bit),title('transmitting of binary'),grid on;axis([0,N*length(sendSignal),-2.5,2.5]);endbpskModu代码function transmittedSignal=bpskModu(signal,bitRate,fc,N)t=linspace(0,1/bitRate,N);c1=sin(2*pi*t*fc);c2=sin(2*pi*t*fc + pi);transmittedSignal=[];for i=1:length(signal)if signal(i)==1transmittedSignal=[transmittedSignal,c1];elsetransmittedSignal=[transmittedSignal,c2];endendfigure(2) % 画调制图plot(1:length(transmittedSignal),transmittedSignal);title('Modulation of BPSK');grid on;figure(3)%画频谱图m=0:length(transmittedSignal)-1;F=fft(transmittedSignal);plot(m,abs(real(F))),title('BPSK_frequency-domain analysis real');grid on;endCheckRatePe代码function PeWrong=CheckRatePe(signal1,signal2,s)rights=0;wrongs=0;for ki=1:s-2if(signal1(ki)==signal2(ki))rights=rights+1;elsewrongs=wrongs+1;endendPeWrong=wrongs/(wrongs+rights);enddemoBPSK代码function bitstream=demoBPSK(receivedSignal,bitRate,fc,n,N)load num%读取num存储的低通滤波用的数据signal1=receivedSignal;t=linspace(0,1/bitRate,N);c=sin(2*pi*t*fc);signal=[];for i=1:nsignal=[signal,c];endsignal2=signal1.*signal; %乘同频同相sinsignal3=filter(num1,1,signal2); %LPF,包络检波3IN=fix(length(num1)/2); %Ñ延迟时间bitstream=[];LL=fc/bitRate*N;i=IN+LL/2;while (i<=length(signal3)) %判决bitstream=[bitstream,signal3(i)>=0];i=i+LL;endfigure(5)subplot(3,1,1);%画接收的包含噪声的波形plot(1:length(signal1),signal1);title('Wave of receiving terminal(including noise)');grid on;subplot(3,1,2);%相干解调波形plot(1:length(signal2),signal2);title('After Multipling sin Fuction');grid on;subplot(3,1,3);%包络检波波形plot(1:length(signal3),signal3);title('Wave of LPF');grid on;bit=[];for i=1:length(bitstream)if bitstream(i)==0bit1=zeros(1,N);elsebit1=ones(1,N);endbit=[bit,bit1];endfigure(6)二进制接收信号波形plot(bit);title('binary of receiving terminal');grid on;axis([0,N*length(bitstream),-2.5,2.5]);endgussian代码function signal=gussian(transmittedSignal,noise)signal=sqrt(2)*transmittedSignal;signal=awgn(signal,noise);figure(4)plot(1:length(signal),signal),grid on;title('Adding noise')end三种调制方式的性能比较:load PeRate;load PeRatep;%补偿误差fpeask(15)=1e-3;fpefsk(9)=1e-3;fpepsk(24)=0.002;fpepsk(26)=1e-3;figure(1)semilogy(-6:length(fpeask)-7,fpeask,-6:length(fpefsk)-7,fpefsk,-30:le ngth(fpepsk)-31,fpepsk),grid on;title('Analysis Of Bit Error Rate');legend('ASK','FSK','PSK');xlabel('r/dB');ylabel('Pe');figure(2)semilogy(-6:length(fpefsk)-7,fpeask);grid on;title('Bit Error Rate Of ASK');xlabel('r/dB');ylabel('PeASK');figure(3)semilogy(-6:length(fpefsk)-7,fpefsk);grid on;title('Bit Error Rate Of FSK');xlabel('r/dB');ylabel('PeFSK');figure(4)semilogy(-16:length(fpepsk)-17,fpepsk);grid on;title('Bit Error Rate Of PSK');axis([-16,10,1e-3,1]);xlabel('r/dB');ylabel('PePSK');三．程序与调制解调波形3.1 2ASK波形1随机信号产生2ASK信号调制3信号噪声附加4接受信号解调5解调出的基带信号3.2．FSK1随机信号产生2FSK信号调制3信号噪声附加4接受信号解调5解调出的基带信号3.3PSK1．随机信号产生2．FSK信号调制3信号噪声附加4接受信号解调5解调出的基带信号3.4误码率分析1.2ASK误码率分析2.2FSK误码率分析3.2PSK误码率分析4性能比较四.课程设计心得体会通过本次的课程设计受益匪浅，感触良多。